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Tycho-Gaia Astrometric Solution (TGAS) parallax data are used to determineabsolute magnitudes $M_V$ for 318 W~UMa-type (EW) contact binary stars. A verysteep (slope $\simeq -9$), single-parameter ($\log{P}$), linear calibration canbe used to predict $M_V$ to about 0.1 -- 0.3 mag over the whole range ofaccessible orbital period, $0.22\!<\!P\!<\!0.88$ days. A similar calibrationfor the most common systems with $0.275\!<\!P\!<\!0.575$ days predicts $M_V$values to about 0.06 -- 0.16 mag. For orbital period values both shorter andlonger than the central range, the period dependence is respectively steeperand shallower, i.e.\ the binaries are fainter in $M_V$ than predicted by thewhole-range, linear law. The steepness of the relation for short-period systemsimplies important consequences for the detectability of the faintest binariesdefining the short-period cut-off of the period distribution. Although thescatter around the linear $\log{P}$-fit is fairly large (0.2 -- 0.4 mag), thecurrent data do not support the inclusion of a $B\!-\!V$ color term in thecalibration.

Absolute Magnitude Calibration for W UMa-Type Systems Based on Gaia Data